FM-index of alignment: A compressed index for similar strings

FM-index of alignment with gaps

“…2. An alignment of similar strings can be compactly represented by combining each common substring α i in all strings as in [15,16,17]. However, the representation is not suitable for the transformed alignment Υ because the characters inα + i are not aligned in Υ.…”

“…To exploit the similarity of the given strings, most of them use classical compression schemes such as run-length encoding and Lempel-Ziv compressions [12,21]. Recently, Na et al [15,16,17] took a new approach using an alignment of similar strings without classical compression schemes, and they proposed indexes of alignment called the suffix tree of alignment [16], the suffix array of alignment (SAA) [17], and the FM-index of alignment (FMA) [15]. The FMA, a compressed version of the SAA, is the most efficient among the three indexes but it is applicable only for an alignment of similar strings without gaps.…”

“…In our index, an alignment is divided into two kinds of regions, common regions and non-common regions, and gaps in a non-common region are put together into one gap in the transformed alignment. The alignment-suffix is defined for the transformed alignment but its definition is different from those defined in [15,16,17]. Due to the alignment transformation and the new definition of the alignment-suffix, our index supports the LF-mapping and backward search, the key functionalities of the FM-index [6,7,8], regardless of gap existence in the alignment.…”

Haplotype-aware graph indexes

“…Text indexes can also take advantage of the alignment by storing shared substrings only once (Huang et al, 2010). The FM-index of alignment (Na et al, 2016(Na et al, , 2018 goes one step further by collapsing the multiple alignment into a directed acyclic graph (DAG), where each node is labeled by a sequence. It indexes the graph and stores some additional information for determining which paths correspond to valid haplotypes.…”

Tunneling on Wheeler Graphs

“…Meanwhile, the concept of Wheeler graphs was introduced by Gagie et al as an alternative way to view Burrows-Wheeler type indices [3]. The framework can be used to derive a number of existing index structures in the Burrows-Wheeler family, like the classical FM-index [4] including its variants for multiple strings [5] and alignments [6], the XBWT for trees [7], the GCSA for directed acyclic graphs [8], and the BOSS data structure for de Bruijn graphs [9].…”